A three way switch on floor one, a 4 way switch on floors 2 through 9, and a 3 way on 10. Bring the feed into the first floor 3 way and feed the light from the 10th floor 3 way. Because you are running the electric about 100 feet, probably should be 12-2 feed on a 20 amp circuit with 12 -3 running from switch one to two, to three, etc, up to switch 10 and than 12-2 to the light. I can diagram it for you if needed.
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